The F-triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the F-triangle explicitly for all irreducible finite root systems. Furthermore, we use these results to partially prove the " F = M Conjecture " of Armstrong which predicts a surprising relation between the F-triangle and the Möbius function of his m-divisible partition poset associated t...

The solution of the equation of heat transfer for pyramidal spines is obtained using computer algebra software. We consider pyramidal spines with three different sectional areas: triangle, square and pentagon. The solutions are given in terms of Bessel functions. From the temperature profiles that were obtained it is possible to deduce explicit formulas for the efficiency of the spine. The resu...

Two generalizations of Sugawara models are discussed. En the first, new interactions are introduced by altering the current commutators but retaining the "free" form of T„„,as exemplified by a simple effective x -2y interaction, which is compared with the standard triangle-diagram results. The second permits nonquadratic T„„,which retain the "algebra" part of the current commutators; these mode...

For an integer w, let Sw be the algebraic triangulated category generated by a w-spherical object. We determine the Picard group of Sw and show that each orbit category of Sw is triangulated and is triangle equivalent to a certain orbit category of the bounded derived category of a standard tube. Moreover, we describe the Ringel–Hall Lie algebra associated to Sw in the sense of Peng and Xiao.

We investigate the problem when tensor functor by a bimodule yields singular equivalence. It turns out that this is equivalent to one Hom given same induces triangle equivalence between homotopy categories of acyclic complexes injective modules. give conditions on appears in pair bimodules, defines with level. construct an explicit combinatorial manner, which quadratic monomial algebra and its ...

We study non-linear traces of the Choquet type and Sugeno on algebra compact operators. They have certain partial additivities. show that these additivities characterize both respectively. There exists a close relation between majorization theory. trace class operators for type. More generally we discuss Schatten–von Neumann p-class determine when they form Banach spaces. This is an attempt at ...

A triangle center such as the incenter, barycenter, etc., is specified by a function thrice- and cyclically applied on sidelengths and/or angles. Consider 1d family of 3-periodics in elliptic billiard, loci its centers. Some will sweep ellipses, others higher-degree algebraic curves. We propose two rigorous methods to prove if locus given an ellipse: one based computer algebra, another algebro-...

In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers with more than 1000 decimal digits. 1 ...

We investigate the triangulated hull of orbit categories perfect derived category and bounded a ring concerning power suspension functor. It turns out that will correspond to full subcategory compact objects certain periodic complexes. This specializes Stai Zhao's result when is finite dimensional algebra with global dimension over field. As first application, if $A,B$ are flat algebras commuta...

We introduce the generalized Serre functor S on a skeletally-small Hom-finite Krull-Schmidt triangulated category C. We prove that its domain Cr and range Cl are thick triangulated subcategories. Moreover, the subcategory Cr (resp. Cl) is the smallest additive subcategory containing all the objects in C which appears as the third term (resp. the first term) of some Aulsander-Reiten triangle in ...